Given: an 802.11 wlan transmitter that emits a 50 mw signal is connected to a cable with 3 db loss. the cable is connected to an antenna with 16 dbi gain. what is the eirp power output?

-- A transmitter has 50 mW output power.  

50 mW is equivalent to +17 dBm.

(+17 is a magic number.  It tells us that the transmitter could very well be based on a single modulated Gunn diode oscillator, which, after resonating and filtering to remove the unwanted puree, hash, and garbage, typically delivers right around +17 dBm at the output.  

-- The power passes through a piece of lossy cable, where it loses 3 dB.

+17 dBm went into the cable.   +14 dBm came out of the other end.  

(The lost 3 dBm warmed the cable.)  

-- The power was then coupled (losslessly) to an antenna with +16 dB "gain".

+14 dBm went into the antenna.  It was shaped and focused so that coming out of the antenna in a certain direction, it sounded as loud as a source that's radiating (+14 + 16) = +30 dBm = 1 watt .

This is NOT 1 watt of real power output.  The antenna has no batteries, it isn't plugged into a wall outlet, and it has no actual 'gain'.  

That 1 watt is "eirp" . . . "Effective Isotropic Radiated Power".  The antenna focuses most of its power in one certain narrow direction, and then, in that direction, it sounds as loud as an antenna would that took 1 watt and spread it equally in all directions.

a straight line sloped